Which of the following numbers is a multiple of 2? ${61,67,110,115,117}$
Solution: The multiples of $2$ are $2$ $4$ $6$ $8$ ..... In general, any number that leaves no remainder when divided by $2$ is considered a multiple of $2$ We can start by dividing each of our answer choices by $2$ $61 \div 2 = 30\text{ R }1$ $67 \div 2 = 33\text{ R }1$ $110 \div 2 = 55$ $115 \div 2 = 57\text{ R }1$ $117 \div 2 = 58\text{ R }1$ The only answer choice that leaves no remainder after the division is $110$ $ 55$ $2$ $110$ We can check our answer by looking at the prime factorization of both numbers. Notice that the prime factors of $2$ are contained within the prime factors of $110$ $110 = 2\times5\times11 2 = 2$ Therefore the only multiple of $2$ out of our choices is $110$. We can say that $110$ is divisible by $2$.